Ed Miliband has rejected the growing clamour for a new investigation into allegations of attempted vote-rigging by the Unite union in the safe Labour seat of Falkirk, saying the latest round of claims do not constitute new evidence.

The findings of an internal inquiry by party officials were thrown into doubt when a key witness appeared to have a change of mind. Unite had been encouraging union members to join the Falkirk Labour Party, where there was a bitter struggle to choose who would be Labour candidate in the 2015 general election.

Two Falkirk residents, Lorraine and Michael Kane, reportedly complained that they had been signed up without their knowledge or consent, but when party officials investigated, they were given a sworn affidavit from Mrs Kane which withdrew the allegation.

On Monday, the Daily Mail reported that they had been told by Mrs Kane that she stood by her original statement. Michael Kane told the BBC: “I gave statements a while ago and that’s it finished with. I never changed nothing.”

This follows the renewed involvement of the police in the internal affairs of the Falkirk Labour Party. Having investigated once, and found nothing that warranted prosecution, they are now looking into emails passed to them last week. The Labour leader has come under heavy pressure to open a second investigation.

The former Chancellor, Alistair Darling, told BBC Scotland that “something had gone very wrong” and that if the police did not decide to investigate, the Labour party should. “The problem with the last report was quite clearly it didn’t have all the facts that are now available,” he said.

“What people will want to know is, in the light of what is now known, with all these emails and everything else, what was going on, who was responsible and what are we going to do about it? Either the police do that, or it has to be done by a separate inquiry.”

The leader of the Scottish Labour Party, Johann Lamont, made a similar call. “We certainly have to look at that because obviously there is a concern if the investigation wasn’t entirely complete,” she said.

But a party spokesman said that Labour’s general secretary, Iain McNicol, had spoken to Mrs Kane after the Mail article and was told by her that she stood by the sworn affidavit that she gave to party officials during their investigation in September.

“We have a sworn affidavit and compared it with a short conversation with a journalist. It is right to base our decision on a sworn affidavit confirmed again today by Mrs Kane,” the spokesman added.

The Falkirk seat has been up for grabs since the sitting MP, Eric Joyce, torpedoed his own political career by starting a fight in a House of Commons bar. Unite was accused of signing up members and paying their fees to secure the position for a former union official, Karie Murphy.